TY - JOUR
T1 - Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties
AU - Li, Wanlin
AU - Mantovan, Elena
AU - Pries, Rachel
AU - Tang, Yunqing
N1 - Publisher Copyright:
© 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo p reduction of certain Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton polygon strata is non-empty. This allows us to give a positive answer, under some compatibility conditions, to a question of Oort about smooth curves in characteristic p whose Newton polygons are an amalgamate sum. As an application, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these arise in inductive systems that demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the 20 special Shimura varieties found in Moonen's work, we prove that all Newton polygon strata intersect the open Torelli locus (if p>>0 in the supersingular cases).
AB - We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo p reduction of certain Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton polygon strata is non-empty. This allows us to give a positive answer, under some compatibility conditions, to a question of Oort about smooth curves in characteristic p whose Newton polygons are an amalgamate sum. As an application, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these arise in inductive systems that demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the 20 special Shimura varieties found in Moonen's work, we prove that all Newton polygon strata intersect the open Torelli locus (if p>>0 in the supersingular cases).
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U2 - 10.1093/imrn/rnaa306
DO - 10.1093/imrn/rnaa306
M3 - Article
AN - SCOPUS:85113437099
SN - 1073-7928
VL - 2022
SP - 6464
EP - 6511
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 9
ER -